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final-rev-big-23998 - Math 1314 Review for Final Exam I...

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Math 1314 Review for Final Exam I. Limits 1. Evaluate: 2 3 lim 2 3 9 x x x →- - + 2. Evaluate: 2 2 4 2 8 lim 16 x x x x - - -
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3. Find 1 1 lim ( ), lim x x f x - + and 1 lim ( ) x f x given the graph below: -4 -3 -2 -1 1 2 3 4 5 -4 -3 -2 -1 1 2 3 4 x y 4. Suppose 2 2 3, 2 ( ) 5, 2 1 3, 1 x x f x x x x + < - = - - Find 2 2 2 1 lim ( ), lim ( ), lim ( ), lim ( ) x x x x f x f x f x f x + - + →- →- →- 1 1 lim ( ), lim ( ) x x f x f x -
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5. Evaluate: 2 2 3 6 3 lim 4 x x x x →∞ - + + . 6. Evaluate: 2 3 lim 5 2 4 x x x x →∞ - - . Find Derivatives 7. Find the derivative: 4 3 2 ( ) 5 3 8 7 1 f x x x x x = - + - +
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8. Find the derivative: 4 ( ) 7 x f x x e x = + + 9. Find the derivative: 2 ( ) ln f x x x =
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10. Find the derivative: ( 2 ( ) ln 4 3 f x x = + 11. Find the derivative: 2 3 ( ) 2 5 x f x x = -
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12. Find the derivative: 4 ( ) 3 x f x e - = 14. Find the second derivative: 3 2 ( ) 3 8 5 3 f x x x x = - + +
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15. Find the second derivative: ( 29 4 5 ( ) 3 f x x = - 16. Find the equation of the line tangent to 3 ( ) 4 5 3 f x x x = - - at the point (-1, 12).
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17. Population is growing according to the model 3 2 1 ( ) 8 9 50 10 P t t t t = - + + + where ( ) P t represents
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